Oscillations

PIRA classification 3A

Please note that these tables have not yet been edited to match the equipment that is available within the UW-Madison lecture demo lab. There maybe many items listed within these tables that we either "can not do" or have available.

A large clock spring oscillates a vertical rod with an adjustable crossbar.

3A10.32

Torsion Pendulum

Calculate angular velocity and acceleration with a large slow torsion pendulum that has movable timer contacts.

3A10.34

crossed dumbell pendulum

Crossed dumbbells with adjustable masses are mounted on an axle as spokes of a wheel. Show the dependence of the period on rotational inertia and on the distance between the center of gravity and axis of the pendulum.

3A10.35

torsion pendulum

Strobe photography of a torsion pendulum.

3A10.40

variable g pendulum

3A10.40

variable g pendulum

A pendulum with a bifilar support of solid rods can be inclined to decrease apparent g.

3A10.40

variable angle pendulum

A physical pendulum is mounted on a bearing so the angle of the plane of oscillation can be changed.

3A10.42

variable g pendulum

Use an electromagnet under the pendulum bob to increase the apparent g.

3A10.42

variable g pendulum

A hidden electromagnet causes a variation in period of a iron pendulum bob.

3A10.44

variable g pendulum

An evaluation of the model M110 Variable g Pendulum manufactured by Physics Apparatus Research Inc. Good pictures of the device for those interested in building their own.

3A10.50

cycloidal pendulum

Demonstrate that a cycloidal pendulum with any amplitude has a period identical to a equal length simple pendulum at small amplitude. Construction details p. 603.

3A10.50

cycloidal pendulum

A pendulum made to swing at large amplitude in the cusp of an inverted cycloid is compared to a simple pendulum.

3A10.55

nonisochronism of pendulum

Two identical pendula, started with large and small amplitudes, have different periods.

3A10.61

sliding pendulum

A block of dry ice is placed on a large parabolic mirror or bent sheet metal trough for other (i.e., cycloidal) curves.

3A15. Physical Pendula

Hang weights from randon holes in the pegboard and mark their paths. Repeat until an intersection point appears. Mark this spot as the center of mass.

PIRA #

Demonstration Name

Subsets

Abstract

3A15.10

physical pendulum

pira200

3A15.10

physical pendulum set

A reconstruction of a nineteenth-century physical pendulum set of four shapes of equal length mounted from a common bar.

3A15.10

other symmetrical shaped pendula

Twenty various physical pendula and are shown.

3A15.12

balancing man physical pendulum

The balancing man usually used to show stable equilibrium is used here as a physical pendulum.

3A15.13

rocking stick

A meter stick with small masses at the ends rocks on a large radius cylinder. Derivation.

3A15.20

oscillating bar

3A15.20

oscillation bar

A bar is suspended from pivots at 1/6 and 1/4 of its length. A companion simple pendulum is used for comparison.

3A15.20

oscillating bar

Analysis of the oscillating bar with a graph of typical data.

3A15.20

oscillating bar

Analysis of the oscillating bar includes suspending the bar from a string.

3A15.20

oscillating bar

Suspend the meter stick from one end and find the center of oscillation with a simple pendulum of the same period.

3A15.20

physical pendulum

Compare the period of a bar supported at the end with a simple pendulum of 2/3 length.

3A15.21

two rods and a ball

A rod pivots at a point 2/3 l, a second rod 2/3 l pivots at the end, and a simple pendulum has length 2/3 l. Then pivot the long rod from the end and compare periods.

3A15.25

oscillating hoop

3A15.25

oscillating hoop

A hoop and pendulum oscillate from the same point.

3A15.25

oscillating hoop

Adjust a simple pendulum to give the same period as a hoop.

3A15.30

paddle oscillator

3A15.30

paddle

A physical pendulum that oscillates with the same frequency from any of a series of holes.

Suspend a meter stick four different ways with the same period of oscillation. Holes are drilled on two concentric circles about the center of mass of a large triangle such that the period of oscillation is always the same.

3A15.35

bent wire

Measure the period of a two corks on a bent wire physical pendulum with the wire bent to various angles.

3A15.40

truncated ring

3A15.40

truncated ring

Same as AJP 35(10),971.

3A15.40

truncated ring

Removing any part of the hoop will not change the period.

3A15.40

hoops and arcs

A hoop oscillates with the same period as arcs corresponding to parts of the hoop.

3A15.45

oscillating lamina

3A15.45

oscillating lamina

Same as TPT 4(2), 78. But where is the reference?

3A15.50

sweet spot

3A15.50

sweet spot

A baseball bat on a frame is rigged to show the motion of the handle end when the bat is hit on and off the center of percussion.

3A15.50

center of percussion

Hang a rod from a thin steel rod that acts as both a support and a pivot. A styrofoam ball on the thin rod is an indicator of the motion of the end of the hanging rod.

3A15.50

sweet spot

Hit a baseball bat on a rail suspension at points on and off the center of percussion.

3A15.50

center of percussion

Hang a long metal bar by a string from one end. Strike the bar with a mallet at various points.

3A15.52

sweet spot

Fire a spring powered gun at a meter stick loosely supported on one end. The top jumps one way or the other when hit off the center of percussion.

3A15.53

sweet spot

Strike a meter stick supported by a matchstick at its center of percussion. Repeat off the center of percussion and break the matchstick. May be scaled up.

3A15.54

sweet spot

A bunch of corks sit on a meter stick on the lecture bench. Hit the stick near the end and as it moves down the table the cork at the center of percussion will remain on the stick.

3A15.55

sweet spot

A rectangular bar suspended by a thread along with an adjustable simple pendulum. Strike the bar.

3A15.55

sweet spot

Strike a heavy metal bar suspended by a string at various points.

3A15.56

sweet spot

A rectangular bar is supported as a physical pendulum from one of two pivots along with a simple pendulum.

3A15.57

sweet spot of a meter stick

3A15.57

sweet spot of a meter stick

3A15.58

sweet spot

A bat is suspended from a horizontal cable under tension. When struck off the center of percussion, vibrations in the cable cause a neon lamp to light.

3A15.59

sweet spot analysis

The different definitions of the term "sweet spot" are discussed, each one based on a different physical phenomenon.

3A15.59

analysis of the sweet spot

Analysis of the three sweet spots of the baseball bat and the location of the impact point that gives maximum power.

3A15.70

Kater's pendulum

3A15.70

Kater's pendulum

Modification of a Welch Kater pendulum so that it may be used more systematically and with improved precision to measure the acceleration due to gravity.

3A15.70

Kater's pendulum

An elaborate pendulum that allows "g" to be determined accurately.

3A15.72

Kater's pendulum

Analysis of: if the center of mass is halfway between the pivots, g cannot be determined from measurements of equal period alone.

3A20. Springs and Oscillators

PIRA #

Demonstration Name

Subsets

Abstract

3A20.10

mass on a spring

pira200

A mass oscillates slowly on a large spring.

3A20.10

mass on a spring

A kg and other masses oscillate on a spring with a constant of about 30 N/m.

3A20.10

mass on a spring

Mass on a spring.

3A20.10

mass on spring

Double the mass on the same spring. Try identical springs in parallel.

3A20.11

bouncing students

Students are bounced from GM car hood springs. Examine the period with different students on board.

3A20.12

mass on a spring

A shortcut method for constructing a vertical spring oscillator of predetermined period.

3A20.13

mass on a spring

Use a slinky for a spring and vary k by using different numbers of turns.

3A20.16

mass on a spring

A discussion of the complexities of the vertical mass on the spring in comparison to the horizontal case.

3A20.20

springs in series and parallel

3A20.20

springs in series and parallel

Hang a mass from a spring, 1/2 mass from two springs in series, and 2m from springs in parallel.

3A20.30

air track glider and spring

An air cart is attached to a single horizontal coil spring.

3A20.30

air track glider and spring

An air cart is attached to a single horizontal coil spring.

3A20.30

air track glider and spring

Horizontal mass and single spring on the air track.

3A20.31

air track glider and spring

Four methods of determining Hooke's law with a air cart and spring.

3A20.35

air track glider between springs

3A20.35

air track glider between springs

3A20.35

air track mass between springs

A mass between two springs on an air track.

3A20.35

air track simple harmonic motion

Place an air track glider between two springs. A video overlay overlay shows the sinusoidal path.

3A20.36

dry ice puck oscillator

A dry ice puck between two springs on a plate of glass. Projection, photocell velocity measurement, etc.

3A20.40

roller cart and spring

3A20.40

roller cart and spring

Attach a large horizontal compression spring to a large heavy roller cart.

3A20.50

oscillating chain

3A20.50

oscillating chain

Tie the ends of a short logging chain with heavy thread and suspend the thread over a pulley.

3A20.50

oscillating chain

A chain suspended on both ends by a string which runs over a pulley.

3A20.50

oscillating chain

Ends of a chain are connected with string and hung over a large pulley.

3A20.55

"U" tube

An open "u" tube filled with mercury.

3A20.60

ball in spherical dish

A ball oscillates in a clear spherical dish on the overhead.

3A20.65

differences in harmonic motion

A plastic hemisphere rocking in water has a higher frequency than when rocking on a level surface.

A device operated with a hand crank causes two small, circular discs to move in simple harmonic motion. One disc moves in a circular path while the other moves in a vertical line showing the physical correspondence of SHM with the "unit" circle (sinusoidal functions).

3A40.20

circular motion vs. pendulum

Shadow project a pendulum and turntable which have identical frequencies.

3A40.20

circular motion vs. pendulum

Shadow project a pendulum and a turntable with a ball mounted on the rim.

3A40.20

pendulum SHM

Shadow project a pendulum and turntable which have identical frequencies.

3A40.20

pendulum SHM

Using a 78 rpm phonograph turntable to synchronize a pendulum and ball on a turntable.

3A40.20

pendulum SHM

A pendulum bob and shadow projection of circular motion of the same frequency appear coupled.

3A40.20

circular motion vs. pendulum

Front view of a marker on a disc and a pendulum.

3A40.21

pendulum SHM

A pendulum bob is shadow projected along with a post rotating on a turntable.

A ball is rolled on a symmetric "U" shaped track to show harmonic motion and compared to a symmetric elongated "U" shape track to show non-harmonic motion.

3A40.25

ball on track vs. pendulum

3A40.27

portulum

In a variation of the simple swinging pendulum, the "portulum", a ball, driven by short blasts of air, rolls along a curved tube. The oscillations of the rolling ball have the same mathematical form as the oscillations of a ball swinging along the same path, but with a lower frequency.

3A40.30

arrow on the wheel

3A40.30

arrow on the wheel

An arrow that can be oriented tangentially or radially is mounted at the edge of a rotating disc and shadow projected on the wall.

3A40.30

arrow on mounted wheel

A large arrow that can be oriented either tangentially or radially is mounted on the periphery of a rotating disc and shadow projected on a screen.

3A40.30

mounted wheel

An arrow at the edge of a rotating disc that can be oriented radially or tangentially is shadow projected onto a wall.

3A40.31

arrow on the wheel

Shadow project a crank handle oriented perpendicular to the wall or screen.

3A40.32

SHM vectors

Three arrows are soldered on a rotating spindle: acceleration, velocity, and displacement vectors. The device is shadow projected on a screen.

3A40.35

SHM slide

3A40.35

SHM slide

A motorized device inserted in a lantern slide projector shows a rotating spot and a SHM spot.

3A70. Coupled Oscillators

A mass on a spring with outriggers is tuned so the three modes of oscillation will couple.

3A70.10

Wilberforce pendulum

The Wilberforce pendulum.

3A70.10

Wilberforce pendulum

Transfer of energy between torsional vibration and vertical oscillation in the Wilberforce pendulum.

3A70.10

Wilberforce pendulum

Shows two Wilberforce pendula.

3A70.10

Wilberforce pendulum

A small Wilberforce pendula.

3A70.10

Wilberforce pendulum

Energy transfers between vertical and torsional modes.

3A70.11

Wilberforce pendulum analysis

Analysis of the Wilberforce pendulum. Compare theory with experiment.

3A70.12

Wilberforce pendulum

Directions for making an inexpensive Wilberforce pendulum, including winding the spring.

3A70.14

swinging mass on a spring

Derivation with the additional hint that you can use a weak spring by adding a length of string to increase the period of the pendulum motion.

3A70.15

swinging mass on a spring

3A70.15

swinging mass on a spring

The oscillation mode of a mass on a spring couples with the pendulum mode.

3A70.15

swinging mass on a spring

Analysis of autoparametric resonance that occurs when the rest length of a spring is stretched by about one third by a mass.

3A70.15

swinging mass on a spring

Oscillations couple if the frequency of a mass on a spring is twice the pendulum mode frequency.

3A70.16

swinging mass on a spring -uncoupled

The special case in which the angular frequency of the spring and the frequency of the pendulum are equal, where the equations of motion actually uncouple and yield independent vertical and pendular motion. The simple apparatus is shown.

3A70.17

spring pendulum

Time the period of a 12" pendulum, take a 12" spring and add mass until the period is the same. Show the extension is 12"

3A70.20

coupled pendula

pira200

Hang two or three pendula from a flexible metal frame.

3A70.20

coupled pendula

Two pendula are hung from a flexible metal frame. A third can be added.

3A70.20

coupled pendula

Two bobs suspended from a suspended horizontal dowel.

3A70.20

coupled pendula

Rods and spring steel support two pendula.

The picture is less than clear.

3A70.21

coupled pendula

There identical pendula are coupled by a slightly flexible support.

3A70.21

coupled pendula

Three identical pendula hang from a slightly flexible stand.

3A70.22

projection coupled pendula

Two small coupled pendula hang from a slightly flexible stand on a clear base.

3A70.25

spring coupled pendula

3A70.25

spring coupled pendula

Two pendula are coupled with a light spring.

3A70.25

spring coupled pendula

Two equal adjustable pendula coupled with a light spring.

3A70.26

spring coupled pendula

Two identical bobs are coupled with a leaf spring.

3A70.27

spring coupled physical pendula

3A70.27

coupled pendula

Two bowling ball bobs on aluminum rods allowing for length adjustments are coupled with a light spring between the rods.

3A70.27

coupled pendula

Two physical pendula are coupled by a spring.

3A70.30

string coupled pendula

3A70.30

string coupled pendula

Pendula are suspended from a horizontal string.

3A70.30

string coupled pendula

Theory and diagram of the string-coupled pendula.

3A70.30

string coupled pendula

Two pendula are coupled on a string. Coupling time depends on the string tightness, amplitude depends on the mass.

3A70.30

string coupled pendula

Two pendula are suspended from a common string.

3A70.31

triple pendula

A spring coupled triple pendulum used to demonstrate the character of normal modes and in particular a mode that has high Q even with the center pendulum highly damped. The mathematically similar to the equations of three coupled quantum mechanical levels.

3A70.32

resonant double pendulum

This double pendulum system with modes that differ by a factor of two has not yet been completely solved.

3A70.33

varied length coupled pendula

A symmetrical arrangement of seven steel balls are coupled 6" below their anchor points with a long wooden bar through which the cords pass. Energy transfers from one end to the other.

3A70.35

double simple pendulum

Analysis of two masses on the same string with combination of the masses and strings being equal or unequal.

3A70.36

over-under pendula

A light pendulum suspended from a heavy pendulum.

3A70.38

electrostatically coupled pendula

Two pith ball pendula couple only when they are charged with the same polarity.

3A70.40

inverted coupled pendula

3A70.40

inverted coupled pendula

Two vertical hacksaw blades with weights at the top are coupled at the bottom.

3A70.41

coupled upside down pendula

Two adjustable upside down pendula are coupled with a rubber band. Also shows beats.

3A70.45

coupled masses on springs

3A70.50

oscillating magnets

3A70.50

oscillating magnets

You really have to see the picture of this to believe it.

3A70.55

coupled compass needles

Oscillations of two compass needles couple.

3A70.56

coupled magnets

Two magnets are suspended from a suspended wooden wand, all horizontal. Oscillations couple and attain a final north-south alignment.

3A70.60

ball & curved track pendulum

Analysis of the peculiar motion of a quarter circle track pendulum with a ball bearing.

3A70.70

rotating 2D coupled oscillations

Examine the oscillations of a "Y" pendulum as it is rotated at varying speeds.

3A75. Normal Modes

PIRA #

Demonstration Name

Subsets

Abstract

3A75.10

coupled harmonic oscillators

Many identical air track gliders are coupled with springs and driven with a variable frequency motor.

3A75.10

coupled harmonic oscillators

Article on identical spring coupled air gliders includes theory.

3A75.10

coupled harmonic oscillators

Several identical air track gliders are coupled with identical springs.

3A75.10

coupled harmonic oscillators

A driven chain of air gliders and springs. Big write up.

3A75.11

coupled harmonic oscillators

Five blocks coupled with coil springs ride in an air trough.

3A75.12

coupled harmonic oscillators

A six meter chain of air supported pucks connected by a slinky.

3A75.12

coupled harmonic oscillators

Six meters of dry ice pucks on a driven slinky.

3A75.30

masses on a string

3A75.30

masses on a string

Clamp 1,2,3, or 4 equal masses to a variably driven wire to show normal modes.

3A75.31

weighted string

Small lead weights on a string driven by a large motor show the lower normal modes of a many body system.

3A75.40

bifilar pendulum modes

3A75.40

bifilar pendulum

All three modes of oscillation are discussed for horizontal rods supported with bifilar suspensions.

3A75.40

bifilar pendulum

Discusses two of three modes - transverse in the plane of the cords and twisting.

3A75.45

selsyn motor pendula

Pendula are hung from the shafts of two selsyn motors. The second mode can be demonstrated.

3A75.50

double pendulum

Normal modes of a two pendula spring coupled driven system.

3A75.80

exposing normal modes

When two modes are simultaneously exited, strobing the system at the frequency of one normal mode will allow the other to be observed independently. A double hacksaw system is used as an example.

3A80. Lissajous Figures

PIRA #

Demonstration Name

Subsets

Abstract

3A80.10

Lissajous sand pendulum

A sand filled compound pendulum traces out a Lissajous pattern.

3A80.10

sand track Lissajous figures

A compound pendulum drops sand out of the pendulum bob in a Lissajous pattern.

3A80.10

Lissajous sand pendulum

A simple sand pendulum made by passing a bifilar suspension through an adjustable collar.

3A80.11

Lissajous figures in sand

A compound pendulum bob traces a Lissajous figure in sand.

3A80.13

Blackburn pendulum

A historical note on Blackburn's role in the "Y suspended" pendulum. ref: AJP 49,452-4

3A80.15

double pendulum "art machine"

Design for a double pendulum machine that draws with a pen.

3A80.15

Lissajous figures - double pendulum

Two adjustable physical pendula at right angles coupled to a pen. Diagram.

3A80.20

Lissajous figures - scope

3A80.20

Lissajous figures - scope

Two generators are fed into the x and y channels of a scope.

3A80.20

Lissajous figures on the scope

Two oscillators generate Lissajous figures of the X and Y channels on an oscilloscope.

3A80.20

Lissajous figures - scope

Use two independent generators to show Lissajous figures on a scope.

3A80.21

Lissajous figures

Lissajous figures on a scope and three other methods in a reprint.

3A80.22

Lissajous figures - scope

Two sine waves are produced by coupling a variable speed motor to one pot in each of two Wheatstone bridge circuits.

3A80.30

Lissajous bar

An oscillating one meter long bar with the width to length ratio a small integer will show a Lissajous pattern when clamped at one end and viewed from the other.

3A80.35

Lissajous figure vibrations

A rectangular cross section rod is mounted vertically and the top is bent over at right angles. When the protruding end is struck it will describe Lissajous patterns.

3A80.40

Lissajous figures - laser

3A80.40

Lissajous figures - projected

Use small mirrors on tuning forks to project a beam of light on the wall.

3A80.41

Lissajous figures - projected

Bounce a laser off a soap film excited by a audio speaker and a Lissajous figure can be projected onto a screen.

3A80.43

Lissajous figures - harmonograph

An elaborate apparatus made to reflect beams off mirrors - two oscillations in SHM and one that is the combination.

3A80.44

Lissajous figures - projected

A sine wave of an integral number of periods is drawn on a clear cylinder. When projected on an overhead, any phase may be obtained by turning the cylinder

3A80.46

Lissajous figures - mechanical

Chains, gears, etc., that allow control of amplitude, initial phase, and frequency of the two component vibrations.

3A80.50

Lissajous figures - 3d

An elaborate setup that uses three motors to produce a spot of light on a card that is the result of three mutually perpendicular SHM's.

3A80.51

Lissajous figures - 3d

A slit in a lantern projector is driven in SHM and the resulting light beam is projected onto a white pencil mounted on a disc rotated by a motor in the perpendicular direction.

3A80.60

textbook corrections

Most Lissajous figures illustrated in textbooks are wrong.

3A80.90

characteristic triangle method

A Lissajous ellipse is drawn using the characteristic triangle method. Fully derived instructions.

3A80.91

Lissajous coordinate system

A coordinate system with the grid proportional to the sines of 0, 30, 60, and 90 degrees is sketched on the board.

3A95. Non-Linear Systems

PIRA #

Demonstration Name

Subsets

Abstract

3A95.10

water relaxation oscillator

A cylinder is filled with water at a constant rate and periodically empties.

3A95.12

electrical and water relaxation osc.

A water relaxation oscillator models a neon flasher relaxation oscillator.

3A95.13

pipet rinser oscillator

The commercial pipet rinser is a much better relaxation oscillator than that in AJP 39(5),575.

3A95.15

wood relaxation oscillator

A wood block rides up and slides back on the inside of a turning hoop.

3A95.20

wood block relaxation oscillator

3A95.20

water feedback oscillator

A tubing and bellows arrangement to generate oscillations by feedback. Picture.

Two springs are attached in a "Y" arrangement, tie a string at two points along a spring so it becomes taut when extended, commercial "constant tension springs".

3A95.28

rubber band oscillations

A review of the foundations a of the rubber band force law and how it applies to the oscillations of a loaded rubber band.

3A95.31

beyond SHM

Shadow project an inertial pendulum onto a selenium photocell and display the resulting voltage on an oscilloscope. Distortion at large amplitude is apparent.

3A95.32

beyond SHM

The design of a pendulum that can demonstrate the dependence of period on amplitude. Common laboratory supplies are used for construction, and timing is done with a stopwatch. Agreement between experimental data and theory to 1 in 1000 is conveniently obtainable.

3A95.32

large amplitude pendulum

Use a rod instead of a string to support the bob and angles can reach 160 degrees. Construction details are given.

3A95.33

pendulum with large amplitude

3A95.33

pendulum with large amplitude

Vary the from 5 to 80 degrees.

3A95.35

non-harmonic air glider

A Jolly balance spring is attached from a point above the middle of an air track to the top of a glider.

3A95.36

nonlinear air track oscillator

A length of rubber perpendicular to the air track axis provides a restoring force. Relative strengths of linear and nonlinear terms can be easily varied.

3A95.37

saline nonlinear oscillator

A small cup with a hole in the bottom and filled with salt water is placed in a large vessel of pure water. The system does all sorts of nonlinear stuff that can be reproduced by numerical simulation.